Let's put it this way as far as moving to Corvallis for medical treatment: there is one decent medical center and school in all of Oregon, in Portland, and it doesn't have one of the 16 specialties evaluated by US News that is ranked ahead of UPMC. That is 80+ miles away from Corvallis for care that is less well regarded in essentially any field that you can think of. Then you have the University of Washington 300 miles north (which is also not generally considered any better than Pitt in most fields) and one of the top Medical Centers in the world is at UCSF, 570 miles south. You know how many world class medical centers are within 300 miles of Pittsburgh? Pitt, Penn, Johns Hopkins, Cleveland Clinic.
Now I have no idea what is wrong with his daughter (or perhaps what happened to her) and I don't really care beyond the fact I'm sorry whatever is happening is happening to someone that was attending Pitt, but he is the one volunteering that she has a medical condition that warrants moving his entire family to Corvallis, Oregon. Much like his pronouncements that he got the "best guy" in his basketball search, the validity of those statements could be absolutely legitimate, but that doesn't stop critical thinking by anyone either just because he has asked for it to stop.
If he wants to leave fine, but bitching about people raising questions about his move and the timing of his move is the nature of his very high profile position. He's a CEO type, where he is compensated among the top of any positions that exist in academia. He is free to reveal a little as he chooses in his private life, but he isn't immune from speculation from those that he has solicited purchases and donations from for two years, particularly since he is abandoning his own major initiatives within the athletic department without seeing them through.